{"title":"Convex expectations for countable-state uncertain processes with càdlàg sample paths","authors":"Alexander Erreygers","doi":"10.1016/j.ijar.2024.109308","DOIUrl":null,"url":null,"abstract":"<div><div>This work investigates convex expectations, mainly in the setting of uncertain processes with countable state space. In the general setting it shows how, under the assumption of downward continuity, a convex expectation on a linear lattice of bounded functions can be extended to a convex expectation on the measurable extended real functions. This result is especially relevant in the setting of uncertain processes: there, an easy way to obtain a convex expectation on the linear lattice of finitary bounded functions is to combine an initial convex expectation with a convex transition semigroup. Crucially, this work presents a sufficient condition on this semigroup which guarantees that the induced convex expectation is downward continuous, so that it can be extended to the set of measurable extended real functions. To conclude, this work looks at existing results on convex transition semigroups from the point of view of the aforementioned sufficient condition, in particular to construct a sublinear Poisson process.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"175 ","pages":"Article 109308"},"PeriodicalIF":3.2000,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Approximate Reasoning","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0888613X24001956","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
引用次数: 0
Abstract
This work investigates convex expectations, mainly in the setting of uncertain processes with countable state space. In the general setting it shows how, under the assumption of downward continuity, a convex expectation on a linear lattice of bounded functions can be extended to a convex expectation on the measurable extended real functions. This result is especially relevant in the setting of uncertain processes: there, an easy way to obtain a convex expectation on the linear lattice of finitary bounded functions is to combine an initial convex expectation with a convex transition semigroup. Crucially, this work presents a sufficient condition on this semigroup which guarantees that the induced convex expectation is downward continuous, so that it can be extended to the set of measurable extended real functions. To conclude, this work looks at existing results on convex transition semigroups from the point of view of the aforementioned sufficient condition, in particular to construct a sublinear Poisson process.
期刊介绍:
The International Journal of Approximate Reasoning is intended to serve as a forum for the treatment of imprecision and uncertainty in Artificial and Computational Intelligence, covering both the foundations of uncertainty theories, and the design of intelligent systems for scientific and engineering applications. It publishes high-quality research papers describing theoretical developments or innovative applications, as well as review articles on topics of general interest.
Relevant topics include, but are not limited to, probabilistic reasoning and Bayesian networks, imprecise probabilities, random sets, belief functions (Dempster-Shafer theory), possibility theory, fuzzy sets, rough sets, decision theory, non-additive measures and integrals, qualitative reasoning about uncertainty, comparative probability orderings, game-theoretic probability, default reasoning, nonstandard logics, argumentation systems, inconsistency tolerant reasoning, elicitation techniques, philosophical foundations and psychological models of uncertain reasoning.
Domains of application for uncertain reasoning systems include risk analysis and assessment, information retrieval and database design, information fusion, machine learning, data and web mining, computer vision, image and signal processing, intelligent data analysis, statistics, multi-agent systems, etc.